Question

Zad.11/112
/-kreska ulamkowa
rozwiąż układy równań:
a)
3(x-1/2)+2(y+3)= 3 ½
3x-1 /3 - y+3/ 2=-1

b)x-3/ 4 - y+5/ 2 =-1.5
x-3/ 2 - 2y-7/ 3=1

c)
2x-5/ 2 - x-6y/ 4= x+y/2
3x-1/10+2y-5/5=2x+y/2

d)
x-3/5-y+1/2=1-(x-y)
4x-1/3-y-3/6=-2(x-y)

Answer 1

Witaj:)
a)
3(x-1/2)+2(y+3)= 3 ½ |*2
3x-1 /3 - y+3/ 2=-1 |*6

6x-3+4y+12=7 |*-1
6x-2-3y-9=-6

-6x-4y -9=-7
6x-3y-11=-6

dodajemy
-6x-4y-9+6x-3y-11=-7+(-6)
-7y=-13+11+9
-7y=7 |:-7
y=-1

podstawiam do rownania
-6x-4y -9=-7
-6x=-7+9+4y
-6x=2+4*(-1)
-6x=2-4
-6x=-2 |:-6
x=1/3


b)x-3/ 4 - y+5/ 2 =-1.5 |*4
x-3/ 2 - 2y-7/ 3=1 |*6

x-3-2y-10=6 |*-2
3x-9-4y+14=6

-2x+6+4y+20=-12
3x-9-4y+14=6

-2x+6+4y+20+3x-9-4y+14=-12+6
x=-6-14+9-20-6
x=-25
podstawiam do rownania
3x-9-4y+14=6
3*(-25)-9-4y+14=6
-4y=6-14+9+75
-4y=76 |:-4
y=19


c)
2x-5/ 2 - x-6y/ 4= x+y/2 |*4
3x-1/10+2y-5/5=2x+y/2 |* 10

4x-10-x+6y=2x+2y
3x-1+4y-10=10x+5y

4x-x-2x-2y=10
3x+4y-10x-5y=10+1

x-2y=10
-7x-y=11 |*-2

x-2y=10
14x+2y=-22

15x=-12
x=-12/15
x=-4/5

x-2y=10

-4/5 - 2y=10
-2y=10+4/5
-2y=54/5 | * -1/2
y= - 27/5




d)
x-3/5-y+1/2=1-(x-y) |*10
4x-1/3-y-3/6=-2(x-y) | 6

2x-6-5y-5=10-10x+10y
8x-2-y+3=-12x+12y

2x-5y+10x-10y=10+5+6
8x-y+12x-12y=2-3

12x-15y=21 |*-5
20x-13y=-1 |*3

-60x+75y=-105
60x-39y=-3
36y=-108
y=-3


20x-13y=-1
20x-13*(-3)=-1
20x+39=-1
20x=-40
x=-2

Answer 2

A)3x-3/2+2y+6=3 1/2
3x-y=-13/6

3x+2y=-1 *(-1)
3x-y=-13/6

-3x-2y=1
3x-y=-13/6
___________
-3y=-7/6
y=-7/18
3x+7/18=-13/6
3x=-13/6-7/18
3x=-39/18-7/18
x=-46/54

b
x-y=-15/10+3/4-5/2
x-2y=1+7/3+3/2

x-y=-130/40 *(-1)
x-2y=29/6

-x+y=130/40
x-2y=29/6
___________
-y=1940/240
y=-1940/240
x-2*(-1940/240)=29/6
x=-1360/120
d
x-y-3/5+1/2=-x+y
4x-y-1/3-3/6=-2x+2y

x-y+x-y=3/5-1/2
4x-y+2x-2y=1/3+3/6

2x-2y=1/10 *(-3)
6x-3y=5/6

-6x+6y=-3/10
6x-3y=5/6
_)______________
3y=32/60
y=32/180
2x-2*(32/180)=1/10
2x-32/90=1/10
2x=1/10+32/90
2x=9/90+32/90
2x=41/90
x=41/80